Topological design of vibrating structures with respect to optimum sound pressure characteristics in a surrounding acoustic medium

Abstract

This paper deals with topological design optimization of vibrating bi-material elastic structures placed in an acoustic medium. The structural vibrations are excited by a time-harmonic external mechanical surface loading with prescribed excitation frequency, amplitude and spatial distribution. The design objective is minimization of the sound pressure generated by the vibrating structures on a prescribed reference plane or surface in the acoustic medium. The design variables are the volumetric densities of material in the admissible design domain for the structure. A high frequency boundary integral equation is employed to calculate the sound pressure in the acoustic field. This way the acoustic analysis and the corresponding sensitivity analysis can be carried out in a very efficient manner. The structural damping is considered as Rayleigh damping. Penalization models with respect to the acoustic transformation matrix and/or the damping matrix are proposed in order to eliminate intermediate material volume densities, which have been found to appear obstinately in some of the high frequency designs. The influences of the excitation frequency and the structural damping on optimum topologies are investigated by numerical examples. Also, the problem of maximizing (rather than minimizing) sound pressures in points on a reference plane in the acoustic medium is treated. Many interesting features of the examples are revealed and discussed.